Problem: Simplify; express your answer in exponential form. Assume $n\neq 0, y\neq 0$. $\dfrac{{(n^{-4}y^{-5})^{5}}}{{(n^{5}y^{-5})^{2}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(n^{-4}y^{-5})^{5} = (n^{-4})^{5}(y^{-5})^{5}}$ On the left, we have ${n^{-4}}$ to the exponent ${5}$ . Now ${-4 \times 5 = -20}$ , so ${(n^{-4})^{5} = n^{-20}}$ Apply the ideas above to simplify the equation. $\dfrac{{(n^{-4}y^{-5})^{5}}}{{(n^{5}y^{-5})^{2}}} = \dfrac{{n^{-20}y^{-25}}}{{n^{10}y^{-10}}}$ Break up the equation by variable and simplify. $\dfrac{{n^{-20}y^{-25}}}{{n^{10}y^{-10}}} = \dfrac{{n^{-20}}}{{n^{10}}} \cdot \dfrac{{y^{-25}}}{{y^{-10}}} = n^{{-20} - {10}} \cdot y^{{-25} - {(-10)}} = n^{-30}y^{-15}$